2 in Binary

To convert the number 2 into binary, we have to follow the following steps:

Step 1: Start by dividing the number (2) by 2, the base of the binary system.
2 ÷ 2 = 1 with a remainder of 0.

Step 2: Write down the remainder (0) as the least significant value (bit) or the rightmost bit of the binary number.

Step 3: Take the quotient (1) and divide it by 2 again:
    1 ÷ 2 = 0 with a remainder of 1.

Step 4: Write down this remainder (1) to the left of the previous bit.

Step 5: Since the quotient is now 0, the process stops

Reading the remainders from bottom to top gives the binary representation of 2 which is, 10.

To understand the concept of binary, let us see the chart of various numbers as to how it is written in binary:

The above table shows the binary conversions of the numbers from 1 to 10. In the above chart, 2 is represented as, 0010 or 10.

2 can be written in binary by using 2 ways, the expansion method and grouping method. Let us now see how we can use these two methods to write 2 in binary.

The step-by-step process of using the expansion method to convert 2 to binary is given below:

Step 1: Understand the binary place values
Binary numbers are expressed as powers of 2. The place values from left to right are:
2⁰ = 1, 2¹ = 2, 2² = 4, 2³ = 8 and so on.

Step 2: Find the largest power of 2 less than or equal to 2
The largest power of 2 that fits into 2 is 2¹ = 2.

Step 3: Write a 1 in that place
Since 2¹ = 2, place a 1 in the 2¹ position.

Step 4: Subtract the value of 2¹ from the number
2 – 2 = 0.

Step 5: Move to the next lower place value (2⁰): 
Since there is no remainder, place a 0 in the position of 2⁰.

Step 6: Write the binary number:
Reading the bits from left to right, the binary number of 2 is 10.

The step-by-step process of using the grouping method to convert 2 to binary is given below:

Step 1: Start with the number
The given number is 2.

Step 2: Divide by 2 and record the remainder
2 ÷ 2 = 0
The remainder is 0
The remainder (0) becomes the rightmost (least significant) bit.

Step 3: Divide the quotient by 2
1 ÷ 2 = 1
The remainder is 1
The remainder (1) becomes the next bit to the left.

Step 4: Group the remainders
Read the remainders from bottom to top: 10

Step 5: Write the binary number
The binary representation of 2 is 10.

There are various rules the students must follow for converting numbers into binary. The rules are as follows:

Rule 1: Place Value Method:

This method involves representing a number as a sum of powers of 2:

• Identify the largest power of 2 which is less than or equal to the given number.

• Subtract the value of this power of 2 from the given number.

• Write a “1” in the binary place corresponding to 21 and “0” for all other powers.

• Repeat the process for all the remaining values until all the powers are used (does not apply to number 0).

Rule 2: Division by 2 Method:

This method involves dividing the number by 2 and then recording the remainders:

• Divide the given number by 2 and note the quotient and remainder.

• Divide the quotient by 2 again and note the new remainder

• Continue dividing the quotient by 2 until the quotient becomes 0

• Write the binary number by reading the remainders from bottom to top.

Rule 3: Representation Method:

This method uses the binary place values directly:

• Write down the powers of 2 in decreasing order, starting from the left.

• Allocate “1” or “0” in each place based on whether the corresponding power of 2 is included in the number.

• Combine the binary digits to form the binary number.

Rule 4: Limitation Rule:

This rule shows the different limitations that occur during binary conversions:

• Finite Representation:
  Only integers can be represented in binary system precisely, fractions require additional complicated methods like binary fractions.

• Memory Limitation:
  Computers have a fixed set of bits to represent binary numbers, if the number is too large it leads to overflow.

• Precision for fractions:
  Non-integers values like 0.1 in decimal cannot be represented precisely in binary, which results in rounding off errors.

• Complexity:
  The conversions of fractions and large numbers can be difficult to compute without additional tools like automation or computational tools.

Understand the Base-2 System:

Unlike our normal number system (Base-10) binary numbers uses only two digits: 0 and 1. Each position of a binary number represents a power of 2.

Master Repeated Division Method:

Students must practice the repeated division method, which is, consistent division of the given number by 2 until the quotient becomes 0. The students must then record the remainders (0 or 1) in each step. The binary number is then read by the remainders from bottom to top. 

Practice with Small Numbers:

Students must learn to always start with small numbers, like from 1 to 20. Then when they understand the concept of conversions, they can move on to larger numbers.

Use Online Calculators (initially):

Students can use calculators to verify their answers and check the manual calculations. The students must analyze how the online converter performs the conversions to gain knowledge of the concept. This tip is only for extra knowledge, do not use the calculators indefinitely as it will hinder the student's manual calculations.

Connect to Real-World Applications:

Students can apply the concept of binary conversions to real-world applications like computer science and electronics. This helps students to understand the concept of binary conversions and how they are used in different fields.

• Binary: A number system that uses two digits: 0 and 1.

• Digit: A single symbol used to represent a number.

• Binary digit (bit): The smallest unit of information in computing, represented by 0 or 1.

• Remainder: The amount left over after division.